Mitigating cross-talk in a flux tunable coupler architecture

ABSTRACT

A method of reducing stray coupling in a qubit array, includes turning ON a first coupler between a first qubit and second qubit of the qubit array by providing a pulse having a first amplitude to the first coupler. A stray coupling between the first coupler and a spectator qubit is reduced by turning ON a second coupler coupled to the spectator qubit, by providing a compensation pulse having a second amplitude, to the second coupler, based on the pulse having the first amplitude.

BACKGROUND Technical Field

The present disclosure generally relates to superconducting devices, andmore particularly, to qubit control.

Description of the Related Art

Superconducting quantum computing is an implementation of a quantumcomputer in superconducting electronic circuits. Quantum computationstudies the application of quantum phenomena for information processingand communication. Various models of quantum computation exist, and themost popular models include the concepts of qubits and quantum gates. Aqubit is a generalization of a bit that has two possible states, but canbe in a quantum superposition of both states. A quantum gate is ageneralization of a logic gate. A quantum gate is a quantum circuitoperating on a small number of qubits, which are building blocks oflarger quantum circuits, like classical logic gates in conventionaldigital circuits. However, the quantum gate describes the transformationthat one or more qubits will experience after the gate is applied onthem, given their initial state. Various quantum phenomena, such assuperposition and entanglement, do not have analogs in the world ofclassical computing and therefore may involve special structures,techniques, and materials.

SUMMARY

According to various embodiments, a method, system, and computing deviceare provided for mitigating stray coupling in a qubit array. A firstcoupler between a first qubit and second qubit of the qubit array isturned ON by providing a pulse having a first amplitude, to the firstcoupler. A stray coupling between the first coupler and a spectatorqubit is reduced, e.g., canceled by turning ON a second coupler coupledto the spectator qubit, by providing a compensation pulse having asecond amplitude, to the second coupler, based on the pulse having thefirst amplitude. By virtue of the compensation pulse provided to thesecond coupler, an adverse interaction with the spectator qubit isavoided during the formation of a gate between the first qubit and thesecond qubit.

In one embodiment, each of the first and second couplers is fluxtunable.

In one embodiment, turning ON the first coupler between the first qubitand the second qubit creates a gate between the first qubit and thesecond qubit. The reduction of the stray coupling between the firstcoupler and the spectator qubit is operative to prevent an accidentalgate between the first qubit and the spectator qubit.

In one embodiment, a width of the compensation pulse is substantiallysimilar to a width of the pulse that is used to turn ON the firstcoupler.

In one embodiment, an amplitude of the compensation pulse is lower thanan amplitude of the pulse that is used to turn ON the first coupler.

In one embodiment, the second coupler is turned ON by the compensationpulse when a frequency of the first qubit is substantially similar to afrequency of the spectator qubit, during a first edge (e.g., risingedge) of the pulse used to turn ON the first coupler.

In one embodiment, the second coupler is turned OFF by the compensationpulse when the frequency of the first qubit is substantially similar tothe frequency of the spectator qubit, during a second edge (e.g.,falling edge) of the pulse used to turn OFF the first coupler.

In one embodiment, the second coupler is turned OFF by the compensationpulse when the frequency of the first qubit is not substantially similarto the frequency of the spectator qubit, during the first edge of thepulse used to turn ON the first coupler.

In one embodiment, the second coupler is turned ON by the compensationpulse when the frequency of the first qubit is substantially similar tothe frequency of the spectator qubit, during the second edge of thepulse used to turn OFF the first coupler.

In one embodiment, a collision between the second qubit and thespectator qubit is prevented by turning ON or keeping ON the secondcoupler by the compensation pulse when a frequency of the second qubitis substantially similar to the frequency of the spectator qubit.

In one embodiment, an amplitude of the compensation pulse, when thefrequency of the first qubit is substantially similar to the frequencyof the spectator qubit, is different from an amplitude of thecompensation pulse when the frequency of the second qubit issubstantially similar to the frequency of the spectator qubit.

In one embodiment, an amplitude of the compensation pulse is determinedby, during a setup phase: applying a series of N pulses to the firstcoupler; for each of the N pulses, sweeping an amplitude of thecompensation signal; and selecting an amplitude of the compensationsignal that provides a least amount of stray coupling between the firstcoupler and the spectator qubit.

In one embodiment, a wait time or Z rotation between each of the Npulses is adjusted based on a highest constructive interference betweentwo compensation pulses.

These and other features will become apparent from the followingdetailed description of illustrative embodiments thereof, which is to beread in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings are of illustrative embodiments. They do not illustrate allembodiments. Other embodiments may be used in addition or instead.Details that may be apparent or unnecessary may be omitted to save spaceor for more effective illustration. Some embodiments may be practicedwith additional components or steps and/or without all the components orsteps that are illustrated. When the same numeral appears in differentdrawings, it refers to the same or like components or steps.

FIG. 1 is an example architecture of a quantum computing system,consistent with an illustrative embodiment.

FIG. 2 is a conceptual block diagram of a plurality of qubits connectedby couplers, consistent with an illustrative embodiment.

FIG. 3 provides a circuit diagram of a plurality of qubits connected bycouplers, consistent with an illustrative embodiment.

FIG. 4 provides a circuit diagram of a plurality of qubits connected bycouplers that are controlled in such a way that stray coupling ismitigated during formation of gates between qubits, consistent with anillustrative embodiment.

FIG. 5 is an example timing operation to reduce an unwanted couplingbetween two qubits during a formation of a gate, consistent with anillustrative embodiment.

FIG. 6 is an example timing operation to reduce multiple collisionsduring a formation of a gate, consistent with an illustrativeembodiment.

FIG. 7 is an example timing diagram that facilitates calibration ofwaveform parameters to minimize leakage during the formation of a gate,consistent with an illustrative embodiment.

FIG. 8 is a conceptual block diagram of complete calibration of thereduction, e.g., cancellation, waveform, consistent with an illustrativeembodiment.

FIG. 9 is an illustrative process related to mitigating stray couplingwith a spectator qubit during the formation of a gate.

FIG. 10 provides a functional block diagram illustration of a computerhardware platform that can be used to implement a particularlyconfigured computing device that can host a qubit cross-talk mitigationengine.

DETAILED DESCRIPTION

Overview

In the following detailed description, numerous specific details are setforth by way of examples to provide a thorough understanding of therelevant teachings. However, it should be apparent that the presentteachings may be practiced without such details. In other instances,well-known methods, procedures, components, and/or circuitry have beendescribed at a relatively high-level, without detail, to avoidunnecessarily obscuring aspects of the present teachings.

In discussing the present technology, it may be helpful to describevarious salient terms. As used herein a qubit represents a quantum bitand a quantum gate is an operation performed on a qubit, such ascontrolling the super-positioning between two qubits.

As used herein, the term C-phase relates to a controlled phase gate,where a Z rotation of one qubit is defined by the state of anotherqubit. A ZZ refers to a state dependent qubit interaction that can beused to form a C-phase gate.

As used herein, the term flux-tunable relates to a device whosefrequency depends on magnetic flux.

As used herein, a transmon is type of superconducting qubit, in whichthe charging energy Ec is much smaller than the Josephson energy Ej.

As used herein, a driveline relates to a qubit control line that carriessignals to the qubit.

As used herein, the term degenerate relates to a quantum mechanicsenergy level that corresponds to two or more different measurable statesof a quantum system. Conversely, two or more different states of aquantum mechanical system are said to be degenerate if they give thesame value energy upon measurement.

Although the terms first, second, third, etc., may be used herein todescribe various elements, these elements should not be limited by theseterms. These terms are only used to distinguish one element fromanother. For example, a first element could be termed a second element,and, similarly, a second element could be termed a first element,without departing from the scope of example embodiments. As used herein,the term “and/or” includes any and all combinations of one or more ofthe associated listed items.

Example embodiments are described herein with reference to schematicillustrations of idealized or simplified embodiments (and intermediatestructures). As such, variations from the shapes of the illustrations asa result, for example, of manufacturing techniques and/or tolerances,may be expected. Thus, the regions illustrated in the figures areschematic in nature and their shapes do not necessarily illustrate theactual shape of a region of a device and do not limit the scope.

It is to be understood that other embodiments may be used and structuralor logical changes may be made without departing from the spirit andscope defined by the claims. The description of the embodiments is notlimiting. In particular, elements of the embodiments describedhereinafter may be combined with elements of different embodiments.

As used herein, certain terms are used indicating what may be consideredan idealized behavior, such as “lossless,” “superconductor,”“superconducting,” “absolute zero,” which are intended to coverfunctionality that may not be exactly ideal but is within acceptablemargins for a given application. For example, a certain level of loss ortolerance may be acceptable such that the resulting materials andstructures may still be referred to by these “idealized” terms.

The present disclosure generally relates to superconducting devices, andmore particularly, to improving integrity of qubits by mitigating straycoupling from dominant qubits that affect spectator qubits duringformation of gates. The electromagnetic energy associated with a qubitcan be stored in so-called Josephson junctions and in the capacitive andinductive elements that are used to form the qubit. In one example, toread out the qubit state, a microwave signal is applied to the microwavereadout cavity that couples to the qubit at the cavity frequency. Thetransmitted (or reflected) microwave signal goes through multiplethermal isolation stages and low-noise amplifiers that are used to blockor reduce the noise and improve the signal-to-noise ratio.Alternatively, or in addition, a microwave signal (e.g., pulse) can beused to entangle one or more qubits. Much of the process is performed ina cold environment (e.g., in a cryogenic chamber), while the microwavesignal of a qubit is ultimately measured at room temperature. Theamplitude and/or phase of the returned/output microwave signal carriesinformation about the qubit state, such as whether the qubit hasdephased to the ground or excited state. The microwave signal carryingthe quantum information about the qubit state is usually weak (e.g., onthe order of a few microwave photons).

To measure this weak signal with room temperature electronics (i.e.,outside the refrigerated environment), low-noise quantum-limitedamplifiers (QLAs), such as Josephson amplifiers and travelling-waveparametric amplifiers (TWPAs), may be used as preamplifiers (i.e., firstamplification stage) at the output of the quantum system to boost thequantum signal, while adding the minimum amount of noise as dictated byquantum mechanics, in order to improve the signal to noise ratio of theoutput chain. In addition to Josephson amplifiers, certain Josephsonmicrowave components that use Josephson amplifiers or Josephson mixerssuch as Josephson circulators, Josephson isolators, and Josephson mixerscan be used in scalable quantum processors.

The ability to include more qubits is salient to being able to realizethe potential of quantum computers. Generally, performance increases astemperature is lowered, for example by reducing the residualthermally-excited state qubit population and decreasing the thermalbroadening of the qubit transition frequencies. Accordingly, the lowerthe temperature, the better for a quantum processor. Further, thecross-talk between an active qubit, sometimes referred to herein as adominant qubit, with adjacent circuitry, such as a coupler resonator ofan adjacent qubit, can increase the error rate. In general, there aretwo main sources of gate errors, namely decoherence (stochastic) andnon-ideal interactions (deterministic). The latter includes parasiticcoupling, leakage to non-computational states, and control crosstalk.For example, the next-nearest neighbor (NNN) coupling is a phenomenonthat is spurious and introduces unwanted interactions between qubitsthat are meant to be unconnected, which is discussed in more detailbelow. NNN as well as any other qubit in the qubit array that may beaffected by stray capacitance during the formation of a gate iscollectively referred to herein as a spectator qubit.

Applicants have recognized that to increase the computational power andreliability of a quantum computer, improvements are needed along twomain dimensions. First, is the qubit count itself. The more qubits in aquantum processor, the more states can in principle be manipulated andstored. Second is low error rates, which is relevant to manipulate qubitstates accurately and perform sequential operations that provideconsistent results and not merely unreliable data. Thus, to improvefault tolerance of a quantum computer, a large number of physical qubitsshould be used to store a logical quantum bit. In this way, the localinformation is delocalized such that the quantum computer is lesssusceptible to local errors and the performance of measurements in thequbits' eigenbasis, similar to parity checks of classical computers,thereby advancing to a more fault tolerant quantum bit. Having one ormore spectator qubits in the proximity of active qubits may exacerbatestray coupling concerns.

In one aspect, the teachings herein are based on Applicants' insightthat directly applying conventional integrated circuit techniques forinteracting with computing elements to superconducting quantum circuitsmay not be effective because of the unique challenges presented byquantum circuits that are not presented in classical computingarchitectures. Accordingly, embodiments of the present disclosure arefurther based on recognition that issues unique to quantum circuits havebeen taken into consideration when evaluating applicability ofconventional integrated circuit techniques to building superconductingquantum circuits, and, in particular, to electing methods andarchitectures used for interacting efficiently with qubits.

Example Architecture

FIG. 1 is an example architecture 100 of a quantum computing system,consistent with an illustrative embodiment. The architecture 100includes a quantum processor 112 comprising a plurality of qubits 114.The quantum processor 112 is located in a refrigeration unit 110, whichmay be a dilution refrigerator. A dilution refrigerator is a cryogenicdevice that provides continuous cooling to temperatures typically 10 mK.Most of the physical volume of the architecture 100 is due to the largesize of the refrigeration unit 110. To reach the near-absolute zerotemperatures at which the system operates, the refrigeration unit 110may us liquid helium as a coolant.

There is a measurement and control unit 130 that is outside of therefrigeration unit 110. The measurement and control unit 130 is able tocommunicate with the quantum processor through an opening 116, sometimesreferred to as a bulkhead of the dilution refrigerator 110, which alsoforms a hermetic seal separating the ambient atmospheric pressure fromthe vacuum pressure of the cryostat under operation.

The plurality of qubits 114 may interact with one another. For example,a gate between qubits 114A and 114B, sometimes referred to herein asnearest neighbors (NN) can be formed. However, stray coupling between adominant qubit (e.g., 114A) and spectator (e.g. 114B) may introduceunwanted interaction resulting in additional errors. In one aspect, twoqubits are coupled together by a tunable coupler bus (e.g., coupler).Applying a flux pulse drives a two qubit Cphase gate. Stray coupling cancreate a significant limit on the gate speed attainable with tunablecouplers. While large coupling (e.g., as much as 300 MHz) has been usedin literature in isolated two qubit experiments, such large coupling mayintroduce high stray coupling between qubits and unconnected couplers(NNN). Such stray coupling may add coherent errors that are typicallyonly present in multiqubit devices (i.e., more than isolated 2 qubits).Accordingly, large coupling is problematic for large multiqubit devices.

Accordingly, in one aspect, the teachings herein substantially reducestray coupling to spectator qubits during two qubit gate operation. Thestray coupling is discussed in more detail below.

Example Block Diagram

FIG. 2 provides a conceptual block diagram 200 of a plurality of qubitsconnected by couplers, consistent with an illustrative embodiment. Morespecifically, FIG. 2 illustrates a first qubit Q₁ (202) and a secondqubit Q₂ (206) being coupled by a first coupler C₁₂ (204). There is athird qubit Q₃ (210) that is coupled to the second qubit Q₂ (206) by wayof a second coupler C₂₃ (208). In one embodiment, each of the couplers204 and 208 are flux tunable, sometimes referred to as tunable busarchitectures. While only three qubits and two couplers have beenillustrated in FIG. 2 to avoid clutter, it will be understood thatadditional qubits and couplers are supported by the teachings herein.

By way of example, consider a gate being performed between the secondqubit Q₂ (206) and the third qubit Q₃ (210). Ideally, the first couplerC₁₂ (204) is in an OFF state, thereby decoupling (e.g., isolating) thefirst qubit Q₁ (202) from the system. In reality, however, there isstray coupling between components. For example, there may be a stray(e.g., capacitive) coupling 220 between the second coupler C₂₃ (208) andthe first qubit Q₁ (202) during the formation of the gate between qubitsQ₃ (210) and Q₂ (206). Similarly, there may be stray coupling 230between the first coupler C₁₂ (204) and the third qubit Q₃ (210) duringa formation of a gate between the first qubit Q₁ (202) and the secondqubit Q₂ (206).

Accordingly, during the formation of the gate between the second qubitQ₂ (206) and the third qubit Q₃ (210), the third qubit Q₃ (210) ishybridized with the second coupler C₂₃ (208). Stray coupling 220 betweenthe second coupler C₂₃ (208) and the first qubit Q₁ (202) results in afinite interaction with the first qubit (202). Consequently, during theformation of this gate, the third qubit Q₃ (210) and the first qubit Q₁(202) can swap excitations. Stated differently, in tunable busarchitectures, stray coupling can give rise to undesired rotations withspectator qubits.

Reference now is made to FIG. 3, which provides a circuit diagram 300 ofa plurality of qubits connected by couplers, consistent with anillustrative embodiment. FIG. 3 illustrates qubits Q₁ (302), Q₂ (304),and Q₃ (306) being coupled by tunable couplers 310 and 320,respectively. While a preferred type of coupler (310, 320) isillustrated by way of example, it will be understood that other types oftunable couplers are supported by the teachings herein as well.

As discussed in the context of FIG. 2 above, when a gate is createdbetween qubit Q₃ (306) and qubit Q₂ (304), coupler C₂₃ (320) is turnedON while other adjacent couplers (e.g., 310) are kept OFF. When a gateis created between qubits Q₁ (302) and Q₂ (304), coupler C₁₂ (310) isturned ON while coupler 320 is kept OFF. Each coupler (e.g., 310) mayhave an antecedent coupler (e.g., JC₁₂ (330)) that is operative toreduce, e.g., cancel, the coupling effect of the coupler C₁₂ (310)between qubits Q₁ (302) and Q₂ (304). For example, antecedent couplerJC₁₂ (330) is tuned such that it has a same magnitude but opposite insign to the coupling effect of its corresponding coupler 310, such thata coupling between the first qubit and the second qubit Q₂ is tuned out.Accordingly, antecedent coupler JC₁₂ is specifically introduced tofacilitate a true OFF state. Similarly, coupler JC₂₃ (340) provides asimilar antecedent coupling for coupler 320. Nonetheless, stray coupling(such as 350) between an active (e.g., ON) coupler 320 and a spectatorqubit (e.g., Q₁ (302)) may result in unreliable performance (e.g.,undesired rotation) of the spectator qubit (e.g., Q₁ (302)). This straycoupling can be tuned out by a specific timing operation of the couplersC₁₂ (310) and C₂₃ (320), where the amplitude and the duration of thetime when these couplers are ON is controlled in particular ways,discussed in more detail below.

Reference now is made to FIG. 4 which provides a circuit diagram of aplurality of qubits connected by couplers that are controlled in such away that stray coupling is mitigated during formation of gates betweenqubits, consistent with an illustrative embodiment. The components ofFIG. 4 are substantially similar to FIG. 3 and are therefore notexplained in detail here for brevity.

By way of example, consider a gate being formed between qubits Q₃ (306)and Q₂ (304). To that end, a first pulse 402 is sent to the coupler C₂₃(320), thereby turning the coupler C₂₃ (320) ON. A second pulse 404,which may have a start time and an end time that is substantiallysimilar to the first pulse 402, is sent to the coupler C₁₂ (310),thereby turning ON coupler C₁₂ (310). In some embodiments, the amplitudeof the pulse 404 is lower than that of pulse 402. Applicants havedetermined that by initiating a small (e.g., smaller than theinteraction between qubits Q₂ (304) and Q₃ (306)) interaction betweenqubit Q₁ (302) and qubit Q₂ (304), the interaction created by the straycoupling 350 is mitigated (e.g., cancelled). Stated differently, straycapacitance between a first coupler (between two dominant qubits) and aspectator qubit during the formation of a gate between the two dominantqubits can be reduced and mitigated by activating (i.e., sending a pulseto) a second coupler C₁₂ (310) to initiate a small interaction betweenthe spectator qubit Q₁ (302) and another qubit (e.g., Q₂ (304)), therebyavoiding adverse interaction with spectator qubits during qubitformation, such as an accidental gate with a spectator qubit.

Example Timing Operation

As mentioned above, in some embodiments, the compensation pulse may beas simple as a scaled (e.g., in amplitude) copy of a pulse that isoperative to turn ON a coupler between two dominant qubits. In oneembodiment, the scaling is set such that the additional interactioncreated by the coupler C₁₂ (310) is equal in size and opposite inmagnitude to the interaction created by action of the coupler C₂₃ (320)acting through the stray coupling 350. However, more advanced timingoperations are possible. A salient insight is that spectator errors tendto be induced via a tunable coupler with a spectator qubit when qubitfrequencies become degenerate. In quantum mechanics, an energy level isdegenerate if it corresponds to two or more different measurable statesof a quantum system. Conversely, two or more different states of aquantum mechanical system are said to be degenerate if they give thesame value of energy upon measurement. It should be noted that turning acoupler ON, can shift the frequencies of the two qubits being coupled.Accordingly, it is possible for qubits that were not degenerate to bedegenerate during part of the pulse.

FIG. 5 is an example timing operation to reduce, e.g., cancel prevent)an unwanted coupling between two qubits during a formation of a gate,consistent with an illustrative embodiment. The waveforms 500 will bediscussed in view of the circuit diagram 300 of FIG. 3. For example,when a gate is formed between qubits Q₃ (306) and Q₂ (304), a pulse(e.g., waveform) 510 is provided to coupler C₂₃ (320). During this pulse(waveform) 510 on coupler C₂₃ (320), both qubit Q₂ and Q₃ frequencieswill change. At some amplitude, Q₁ and Q₃ will be degenerate allowingfor a swap (e.g., a type of an unwanted gate). For example, thefrequency of both qubits Q₁ (302) and Q₃ (306) will be equal. It isduring this phase (i.e., when the frequencies of both qubits beingsubstantially similar) that accidental swaps can occur and spectatorqubits are most vulnerable. In this regard, to reduce, e.g., cancel, acollision between qubit Q₃ (306) and Q₁ (302) facilitated by a straycoupling 350 between qubit Q₁ (302) and coupler C₂₃ (320), a pulse 512is applied to coupler C₁₂ (310) such that, at the time when thecollision occurs, the coupling between qubits Q₃ (306) and Q₁ (302) iscanceled. As illustrated by waveform 512, the waveform applied to thesecond coupler C₁₂ (310) need not be a copy of the waveform applied toqubit C₂₃ (320). Rather, in one embodiment, the waveform 512 can be aspecially crafted pulse that reaches an appropriate amplitude forreduction, e.g., cancelation, of the stray coupling 350 just during arelevant time. This relevant time is the period when the frequencydifference between the dominant qubit Q₃ (306) and the spectator qubitQ₁ (302) is comparable (e.g., within a predetermined range) tointeraction strength created by the stray coupling. When the frequencyof the qubit Q₃ (306) exits this condition, the coupler C₁₂ (310) isturned OFF. A similar operation is performed during the next edge (e.g.,falling edge) of the waveform 510. In this way, a more precise (i.e.,time targeted) ON and OFF time of the second coupler is provided, whichprevents collision between qubits Q₃ (306) and Q₁ (302), while reducingZZ (a state dependent qubit interaction that can be used to form aC-phase gate), as compared to waveform 404 in FIG. 4.

The teachings herein are not limited to preventing single collisions. Inthis regard, reference is made to FIG. 6, which is an example timingoperation to reduce, e.g., cancel (prevent), multiple collisions duringa formation of a gate, consistent with an illustrative embodiment. Thewaveforms 600 will be discussed in view of the circuit diagram 300 ofFIG. 3. Multiple collisions can occur when there are more than onespectator qubits that could be affected by the stray capacitanceintroduced during the formation of a gate between two dominant qubits(e.g., Q₃ (306) and Q₂ (304)). Typically, such collisions can occur indifferent manifolds, namely, with only qubit Q₃ (306) or qubit Q₁ (302)in excited state (i.e., 1 photon manifold) vs. with qubits Q₂ (304) andQ₃ (306) excited (i.e., 2 photon manifold).

Different collisions can have different reduction, e.g., cancelation,conditions. However, different collisions are also encountered atdifferent amplitudes of the C₂₃ (320) coupler. As a result, acancellation waveform can be created that accommodates more than onecollision during the formation of a gate. For example, when a gate isformed between qubits Q₃ (306) and Q₂ (304), a pulse (e.g., waveform)610 is provided to coupler C₂₃ (320) having a first amplitude 650.During this pulse (waveform) 610 on coupler C₂₃ (320), both qubit Q₂(304) and Q₃ (306) frequencies will change. At some amplitude, Q₁ and Q₃will be degenerate allowing for a swap (e.g., accidental gate). At time602, the frequency of both qubits Q₁ (302) and Q₃ (306) will be equal.To reduce, e.g., cancel a collision between qubit Q₃ (306) and Q₁ (302)facilitated by a stray coupling 350 between qubit Q₁ (302) and couplerC₂₃ (320), a pulse 612 having a second amplitude 652. Accordingly, atthe time that the collision occurs between the qubits Q₁ (302) and Q₃(306), the coupling between the same is cancelled. However, at time 604,there is a collision between the qubits Q₂ (304) and Q₁ (302). In thisregard, to cancel a collision between qubits Q₂ (304) and Q₁ (302)facilitated by a stray coupling between qubit Q₁ (302) and coupler C₁₂(310), a pulse 612 having a third amplitude 654. A similar operation isperformed during the next edge (e.g., falling edge) of the waveform 610.

Example Calibration of Compensation Waveform

Accordingly, the shape of the compensation waveform can preventundesired rotations in spectator qubits during the formation of a gatebetween dominant qubits. FIG. 7 is an example timing diagram 700 thatfacilitates calibration of waveform parameters to minimize leakageduring the formation of a gate, consistent with an illustrativeembodiment. The waveforms 710 and 712 will be discussed in view of thecircuit diagram 300 of FIG. 3.

Waveform 710 represents the activation cycle of the coupler C₂₃ (320) tofacilitate the creation of a gate between qubits Q₂ (304) and Q₃ (306).A series of N pulses is applied on the coupler C₂₃ (320) along with acompensation waveform to the coupler C₁₂ (310) to compensate for thestray coupling 350 between the spectator qubit Q₁ (302) and the couplerC₂₃ (320). The compensation waveform 712 applied to the second couplerC₁₂ (310) between the spectator qubit Q₁ (302) and the second qubit Q₂(304) is varied in at least one of amplitude or pulse width in eachcycle to determine at least one of: (i) a time to initiate the pulse(e.g., positive ramp), (ii) a pulse width (e.g., when to initiate anegative ramp), and (iii) an amplitude of the pulse of the compensationwaveform 712. These parameters are optimized to minimize any swapping ofexcitations between relevant qubits (e.g., Q₃ (306) and Q₁ (302)). Forexample, the measurement & control unit 130 may adjust a parameter foreach pulse and measure an amount of leakage (e.g., how it affects aspectator qubit) and create a plot thereof. The point that provides aminimum amount of leakage is selected for that particular parameter.Other parameters may be adjusted similarly until all parameters areadequately adjusted to provide an appropriate initiation time, pulsewidth, and/or amplitude for the compensation signal 712.

In one embodiment, a pulse wait time 720 is adjusted between the pulsesof waveform 710 to improve contrast. The wait time between pulseschanges the contrast. For example, between pulses of the waveform 710,there is a frequency difference between swapped and non-swapped states.This frequency difference results in a phase difference that can lead toeither constructive (higher contrast) or destructive (lower contrast)interference between successive pulses. In this regard, in oneembodiment, the measurement and control unit 130 may perform a sweep ofthe wait time 720 to identify a wait time 720 that provides aconstructive interference between pulses, thereby leading to highercontrast.

FIG. 8 is a conceptual block diagram 800 of complete calibration of thereduction, e.g., cancelation waveform, consistent with an illustrativeembodiment. The block diagram 800 will be discussed with reference toFIG. 1.

At block 801, a blind sweep is performed by the measurement and controlunit 130. For example, a reduction, e.g., cancelation, amplitude isswept. This sweep is “blind” in the sense that a proper wait time hasnot yet been determined. Consequently, the measurement contrast can bepoor (e.g., not optimized). In this regard, at block 802 a wait sweep isperformed. For example, with the reduction, e.g., cancelation, amplitudechosen to be close to optimal in block 801, wait time (720) is swept. Apoint with the most contrast is selected, thereby providing constructiveinterference. At block 803, a non-blind sweep is performed for theparameters of the second coupler (e.g., coupled to the spectator qubit),where the wait time from the wait sweep 802 is used. The optimization ofwait time provides enhanced contrast and thus allows to find an optimumcancelation amplitude in the presence of noise. In one embodiment, therole of the wait time can be substituted with Z rotations on one or bothof the qubits involved.

Example Process

With the foregoing overview of the example architectures, it may behelpful now to consider a high-level discussion of an example process.To that end, FIG. 9 presents an illustrative process related tomitigating stray coupling with a spectator qubit during the formation ofa gate. Processes 900 is illustrated as a collection of blocks, in alogical flowchart, which represents a sequence of operations that can beimplemented in hardware, software, or a combination thereof. In thecontext of software, the blocks represent computer-executableinstructions that, when executed by one or more processors, perform therecited operations. Generally, computer-executable instructions mayinclude routines, programs, objects, components, data structures, andthe like that perform functions or implement abstract data types. Ineach process, the order in which the operations are described is notintended to be construed as a limitation, and any number of thedescribed blocks can be combined in any order and/or performed inparallel to implement the process. In various embodiments, the processmay be controlled in a cryogenic environment or at room temperature by ameasurement and control unit 130 of FIG. 1. For discussion purposes, theprocess is described with reference to the architecture of FIG. 3.

At block 902, a qubit cross-talk mitigation engine, which may be part ofthe measurement and control unit 130, turns ON a first coupler C₂₃ (320)between a first qubit Q₃ (306) and second qubit Q₂ (304) of the qubitarray by providing a pulse having a first amplitude to the first couplerC₂₃ (320). Turning ON the first coupler first coupler C₂₃ (320) betweenthe first qubit Q₃ (306) and second qubit Q₂ (304) creates a gatebetween them.

At bock 904, a stray coupling between the first coupler C₂₃ (320) and aspectator qubit Q₁ (302) is reduced, e.g., cancelled, by turning ON asecond coupler C₁₂ (302) coupled to the spectator qubit Q₁ (302), byproviding a compensation pulse having a second amplitude, to the secondcoupler second coupler C₁₂ (302), based on (a timing of) the firstpulse. As explained in the context of the discussion of FIGS. 4 to 7,the timing of the compensation pulse is based on the timing of the firstpulse. In various embodiments, the compensation pulse may be a simpleclone of the first pulse at an appropriate amplitude, or may have adifferent shape to further reduce noise and/or to accommodate anyadditional collisions with spectator qubits. The first and secondcouplers are flux tunable. The reduction, e.g., cancellation, of thestray coupling 350 between the first coupler C₂₃ (320) and the spectatorqubit Q₁ (302) is operative to prevent an accidental gate between thesequbits.

Example Computer Platform

As discussed above, functions relating to interacting with qubits by wayof measurement and control signals may include a measurement and controlunit, as shown in FIG. 1. FIG. 10 provides a functional block diagramillustration of a computer hardware platform 1000 that can be used toimplement a particularly configured computing device that can host aqubit cross-talk mitigation engine 1040 operative to perform thefunctions discussed herein. In particular, FIG. 10 illustrates a networkor host computer platform 1000, as may be used to implement anappropriately configured computing device, such as the measurement andcontrol block 130 of FIG. 1.

The computer platform 1000 may include a central processing unit (CPU)1004, a hard disk drive (HDD) 1006, random access memory (RAM) and/orread only memory (ROM) 1008, a keyboard 1010, a mouse 1012, a display1014, and a communication interface 1016, which are connected to asystem bus 1002.

In one embodiment, the HDD 1006, has capabilities that include storing aprogram that can execute various processes, such as the qubit cross-talkmitigation engine 1040, in a manner described herein. The qubitcross-talk mitigation engine 1040 may have various modules configured toperform different functions. For example, there may be a pulse widthmodule 1042 operative to determine a start and stop time of acompensation pulse that mitigates stray coupling, based on a timing of apulse applied to a coupler used in creating a gate between two qubits.There may be an amplitude module 1044 operative to provide anappropriate amplitude of the compensation signal based on a collisiontime between a dominant qubit and a spectator qubit as described herein.There may be a wait time module 1046 operative to adjust a wait timebetween pulses applied to couplers during formation of gates, such thatan appropriate contrast is achieved between pulses. There may be acompensation timing module 1048 operative to determine a start and stoptime of a compensation pulse that mitigates stray coupling, based onwhen collisions occur between dominant qubits and spectator qubits.

CONCLUSION

The descriptions of the various embodiments of the present teachingshave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

While the foregoing has described what are considered to be the beststate and/or other examples, it is understood that various modificationsmay be made therein and that the subject matter disclosed herein may beimplemented in various forms and examples, and that the teachings may beapplied in numerous applications, only some of which have been describedherein. It is intended by the following claims to claim any and allapplications, modifications and variations that fall within the truescope of the present teachings.

The components, steps, features, objects, benefits and advantages thathave been discussed herein are merely illustrative. None of them, northe discussions relating to them, are intended to limit the scope ofprotection. While various advantages have been discussed herein, it willbe understood that not all embodiments necessarily include alladvantages. Unless otherwise stated, all measurements, values, ratings,positions, magnitudes, sizes, and other specifications that are setforth in this specification, including in the claims that follow, areapproximate, not exact. They are intended to have a reasonable rangethat is consistent with the functions to which they relate and with whatis customary in the art to which they pertain.

Numerous other embodiments are also contemplated. These includeembodiments that have fewer, additional, and/or different components,steps, features, objects, benefits and advantages. These also includeembodiments in which the components and/or steps are arranged and/orordered differently.

Aspects of the present disclosure are described herein with reference toa flowchart illustration and/or block diagram of a method, apparatus(systems), and computer program products according to embodiments of thepresent disclosure. It will be understood that each block of theflowchart illustrations and/or block diagrams, and combinations ofblocks in the flowchart illustrations and/or block diagrams, can beimplemented by computer readable program instructions.

These computer readable program instructions may be provided to aprocessor of an appropriately configured computer, special purposecomputer, or other programmable data processing apparatus to produce amachine, such that the instructions, which execute via the processor ofthe computer or other programmable data processing apparatus, createmeans for implementing the functions/acts specified in the flowchartand/or block diagram block or blocks. These computer readable programinstructions may also be stored in a computer readable storage mediumthat can direct a computer, a programmable data processing apparatus,and/or other devices to function in a manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The call-flow, flowchart, and block diagrams in the figures hereinillustrate the architecture, functionality, and operation of possibleimplementations of systems, methods, and computer program productsaccording to various embodiments of the present disclosure. In thisregard, each block in the flowchart or block diagrams may represent amodule, segment, or portion of instructions, which comprises one or moreexecutable instructions for implementing the specified logicalfunction(s). In some alternative implementations, the functions noted inthe blocks may occur out of the order noted in the Figures. For example,two blocks shown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts or carry outcombinations of special purpose hardware and computer instructions.

While the foregoing has been described in conjunction with exemplaryembodiments, it is understood that the term “exemplary” is merely meantas an example, rather than the best or optimal. Except as statedimmediately above, nothing that has been stated or illustrated isintended or should be interpreted to cause a dedication of anycomponent, step, feature, object, benefit, advantage, or equivalent tothe public, regardless of whether it is or is not recited in the claims.

It will be understood that the terms and expressions used herein havethe ordinary meaning as is accorded to such terms and expressions withrespect to their corresponding respective areas of inquiry and studyexcept where specific meanings have otherwise been set forth herein.Relational terms such as first and second and the like may be usedsolely to distinguish one entity or action from another withoutnecessarily requiring or implying any actual such relationship or orderbetween such entities or actions. The terms “comprises,” “comprising,”or any other variation thereof, are intended to cover a non-exclusiveinclusion, such that a process, method, article, or apparatus thatcomprises a list of elements does not include only those elements butmay include other elements not expressly listed or inherent to suchprocess, method, article, or apparatus. An element proceeded by “a” or“an” does not, without further constraints, preclude the existence ofadditional identical elements in the process, method, article, orapparatus that comprises the element.

The Abstract of the Disclosure is provided to allow the reader toquickly ascertain the nature of the technical disclosure. It issubmitted with the understanding that it will not be used to interpretor limit the scope or meaning of the claims. In addition, in theforegoing Detailed Description, it can be seen that various features aregrouped together in various embodiments for the purpose of streamliningthe disclosure. This method of disclosure is not to be interpreted asreflecting an intention that the claimed embodiments have more featuresthan are expressly recited in each claim. Rather, as the followingclaims reflect, inventive subject matter lies in less than all featuresof a single disclosed embodiment. Thus, the following claims are herebyincorporated into the Detailed Description, with each claim standing onits own as a separately claimed subject matter.

What is claimed is:
 1. A method of reducing stray coupling in a qubitarray, comprising: turning ON a first coupler between a first qubit andsecond qubit of the qubit array by providing a pulse having a firstamplitude, to the first coupler; reducing a stray coupling between thefirst coupler and a spectator qubit by turning ON a second couplercoupled to the spectator qubit, by providing a compensation pulse havinga second amplitude, to the second coupler, based on the pulse having thefirst amplitude.
 2. The method of claim 1, wherein each of the first andsecond couplers is flux tunable.
 3. The method of claim 1, whereinturning ON the first coupler between the first qubit and the secondqubit creates a gate between the first qubit and the second qubit. 4.The method of claim 3, wherein the reduction of the stray couplingbetween the first coupler and the spectator qubit is operative toprevent an accidental gate between the first qubit and the spectatorqubit.
 5. The method of claim 1, wherein a width of the compensationpulse is substantially similar to a width of the pulse that is used toturn ON the first coupler.
 6. The method of claim 5, wherein anamplitude of the compensation pulse is lower than an amplitude of thepulse that is used to turn ON the first coupler.
 7. The method of claim1, wherein the second coupler is turned ON by the compensation pulsewhen a frequency of the first qubit is substantially similar to afrequency of the spectator qubit, during a first edge of the pulse usedto turn ON the first coupler.
 8. The method of claim 7, wherein thesecond coupler is turned OFF by the compensation pulse when thefrequency of the first qubit is substantially similar to the frequencyof the spectator qubit, during a second edge of the pulse used to turnOFF the first coupler.
 9. The method of claim 8, wherein the secondcoupler is turned OFF by the compensation pulse when the frequency ofthe first qubit is not substantially similar to the frequency of thespectator qubit, during the first edge of the pulse used to turn ON thefirst coupler.
 10. The method of claim 9, wherein the second coupler isturned ON by the compensation pulse when the frequency of the firstqubit is substantially similar to the frequency of the spectator qubit,during the second edge of the pulse used to turn OFF the first coupler.11. The method of claim 9, further comprising, preventing a collisionbetween the second qubit and the spectator qubit by turning or keepingON the second coupler by the compensation pulse when a frequency of thesecond qubit is substantially similar to the frequency of the spectatorqubit.
 12. The method of claim 11, wherein an amplitude of thecompensation pulse, when the frequency of the first qubit issubstantially similar to the frequency of the spectator qubit, isdifferent from an amplitude of the compensation pulse when the frequencyof the second qubit is substantially similar to the frequency of thespectator qubit.
 13. The method of claim 1, further comprisingdetermining an amplitude of the compensation pulse by, during a setupphase: applying a series of N pulses to the first coupler; for each ofthe N pulses, sweeping an amplitude of the compensation signal; andselecting an amplitude of the compensation signal that provides a leastamount of stray coupling between the first coupler and the spectatorqubit.
 14. The method of claim 1, further comprising adjusting a waittime or Z rotation between each of the N pulses based on a highestconstructive interference between two compensation pulses.
 15. Acomputing device comprising: a processor; a storage device coupled tothe processor; an engine stored in the storage device, wherein anexecution of the engine by the processor configures the computing deviceto perform acts, comprising: turning ON a first coupler between a firstqubit and second qubit of a qubit array by providing a pulse having afirst amplitude to the first coupler; reducing a stray coupling betweenthe first coupler and a spectator qubit by turning ON a second couplercoupled to the spectator qubit, by providing a compensation pulse havinga second amplitude, to the second coupler, based on the pulse having thefirst amplitude.
 16. The computing device of claim 15, wherein: theturning ON of the first coupler between the first qubit and the secondqubit creates a gate between the first qubit and the second qubit; andthe reduction of the stray coupling between the first coupler and thespectator qubit is operative to prevent an accidental gate between thefirst qubit and the spectator qubit.
 17. The computing device of claim15, wherein: a width of the compensation pulse is substantially similarto a width of the pulse that is used to turn ON the first coupler; andan amplitude of the compensation pulse is lower than an amplitude of thepulse that is used to turn ON the first coupler.
 18. The computingdevice of claim 15, wherein: the second coupler is turned ON by thecompensation pulse when a frequency of the first qubit is substantiallysimilar to a frequency of the spectator qubit, during a first edge ofthe pulse used to turn ON the first coupler; and the second coupler isturned OFF by the compensation pulse when the frequency of the firstqubit is substantially similar to the frequency of the spectator qubit,during a second edge of the pulse used to turn OFF the first coupler.19. The computing device of claim 18, wherein: the second coupler isturned OFF by the compensation pulse when the frequency of the firstqubit is not substantially similar to the frequency of the spectatorqubit, during the first edge of the pulse used to turn ON the firstcoupler; and the second coupler is turned ON by the compensation pulsewhen the frequency of the first qubit is substantially similar to thefrequency of the spectator qubit, during the second edge of the pulseused to turn OFF the first coupler.
 20. The computing device of claim19, wherein the execution of the engine by the processor furtherconfigures the computing device to perform acts comprising preventing acollision between the second qubit and the spectator qubit by turning orkeeping ON the second coupler, by the compensation pulse, when afrequency of the second qubit is substantially similar to the frequencyof the spectator qubit.